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        "title": "Leonhard Euler, De summis serierum reciprocarum, E41 (1735/1740), translation by Jordan Bell",
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            "citation": "Leonhard Euler, De summis serierum reciprocarum, E41 (1735/1740), translation by Jordan Bell",
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      "statement": "# Euler: the reciprocal-square sum and the circle constant\n\nEuler evaluated the sum of reciprocal squares of the positive integers as π²/6. His E41 paper developed connections between even reciprocal-power series and trigonometric expansions.\n\nA simple arithmetic series had resisted an exact expression. Euler related its sum to the circle constant through trigonometric expansions and their roots. The surviving paper identifies a specific analytic result and historical derivation, independently of the bridges problem.\n\n## Scientific scope\n\nThis is a historical evaluation without an independent WRS proof audit. The paper's infinite factor reasoning is its original derivation; no claim is made that odd reciprocal-power sums were all evaluated.\n\n## People and systems\n\nLeonhard Euler\n\n\n\n## Original sources\n\n- [Leonhard Euler, De summis serierum reciprocarum, E41 (1735/1740), translation by Jordan Bell](https://arxiv.org/abs/math/0506415)\n",
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    "title": "Euler: the reciprocal-square sum and the circle constant",
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